The disclosure of the present application relates generally to medical imaging, and more particularly, to mapping of the vascular system.
Analysis of spatial perfusion of blood flow of any organ requires detailed morphometry on the geometry (including, but not limited to, diameters, lengths, number of vessels, etc.) and the corresponding branching patterns (including, but not limited to, three-dimensional (3D) angles, connectivity of vessels, etc.). Despite the significance of morphometric data for understanding spatial distribution of blood flow and hemodynamics, the data are relatively sparse. One of the major reasons for the scarcity of morphometric data is the tremendous labor required to obtain such data. Reconstructing and counting a significant number of vessels in most organs is an extremely labor-intensive endeavor. As such, what is needed to accomplish the same result is the development of a labor-saving methodology.
Several approaches for extracting curve-skeletons or medial axes can be found in the literature. Different studies can be found on segmentation of volumetric data sets. Representative approaches include surface extraction based on an energy function using the image gradient, deformable meshes, hysteresis thresholding and region growing, m-reps, skeletons composed of atoms (hubs) connected to the surface, and distance to the vessel wall combined with a penalty function. For example, and to improve the segmentation, Lei et al. (Artery-vein separation via MRA—An image processing approach. IEEE Trans Med Imaging, 20(8):689-703, 2001) deployed fuzzy connectedness to segment vessels and distinguish between arteries and veins, while Chung et al. (Vascular segmentation of phase contrast magnetic resonance angiograms based on statistical mixture modeling and local phase coherence. IEEE Trans Med Imaging, 23(12):1490-1507, 2004) used different mixture models. Gan et al. (Statistical cerebrovascular segmentation in three-dimensional rotational angiography based on maximum intensity projections. Med Phys., 32(9):3017-3028, 2005) analyzed the maximum intensity distribution to identify optimal thresholds to extract vessels from a series of maximum intensity projections. By using an atlas, Passat et al. (Region-growing segmentation of brain vessels: An atlas-based automatic approach. J Magn Reson Imaging., 21(6):715-725, 2005) divided the human brain into different areas to optimize a region growing segmentation of brain vessels. Subsequently, the atlas was refined by adding morphological data, such as vessel diameter and orientation, to extract a vascular tree from phase contrast MRA data. Centerlines extracted using the algorithm by Aylward et al. (Initialization, noise, singularities, and scale in height ridge traversal for tubular object centerline extraction. IEEE Trans Med Imaging, 21(2):61-75, 2002) based on intensity ridge traversal were smoothed using a B-spline-based approach to get smoother results. Zhang et al. (Automatic detection of three-dimensional vascular tree centerlines and bifircations in high-resolution magnetic resonance angiography. Invesi Radiol., 40(10):661-671, 2005) described a centerline extraction algorithm based on Dijkstra's algorithm using a distance-field cost function. The jagged lines that typically result from voxel-based centerline extraction algorithms were smoothed using either cubic splines or Chebyshev polynomials. Other artifacts from the results of a 3D thinning algorithm, such as cycles, spurs, and non-unit-width parts, can be removed by using an approach by Chen et al. (Automatic 3D vascular tree construction in CT angiography. Comput Med Imaging Graph., 27(6):469-479, 2003). Ukil et al. (Smoothing lung segmentation surfaces in three-dimensional X-ray CT images using anatomic guidance. Acad Radiol., 12(12):1502-1511, 2005) introduced a smoothing approach for airways of a lung based on an ellipsoidal kernel before segmenting and thinning the 3D volumetric image.
To describe a geometric model of the vessels of brain data sets, Volkau et al. (Geometric Modeling of the Human Normal Cerebral Arterial System. IEEE Transactions on Medical Imaging, 24(4):529-539, 2005) used the centerline and radii to describe cylinders. The centerlines were smoothed using average filtering to avoid self-intersections of the cylinders. The surfaces of the cylinders were modeled following a Catmull-Clark sub-division surface approach. For extracting centerlines from volumetric images, topology- or connectivity-preserving thinning is a common approach. By using the Hessian of the image intensity, Bullet et al. (Symbolic description of intracerebral vessels segmented from magnetic resonance angiograms and evaluation by comparison with X-ray angiograms. Med Image Anal., 5(2):157-169, 2001) developed a ridge line detection method to identify centerlines. Once the centerline is determined, quantitative data, such as lengths, areas, and angles, can be extracted as shown by Martinez-Perez et al. (Retinal vascular tree morphology: a semi-automatic quantification. IEEE Trans Biomed Eng., 49(8):912-917, 2002) and Wan et al. (Multi-generational analysis and visualization of the vascular tree in 3D micro-CT images. Comput Biol Med., 32(2):55-71, 2002). A detailed data structure for building an airway tree was described by Chaturvedi et al. (Three-dimensional segmentation and skeletonization to build an airway tree data structure for small animals. Phys Med Biol., 50(7):1405-1419, 2005). Recently, Nordsletten et al. (Structural morphology of renal vasculature. Am J Physiol Heart Circ Physiol., 291(1):H296-309, 2006) proposed an approach that segments vessels of rat kidney based on iso-surface computation. Using the surface normals, the surface projects to the center of the vessels, while a snake algorithm collects and connects the resulting point cloud. To analyze the branching morphology of the rat hepatic portal vein tree, Den Buijs et al. (Branching morphology of the rat hepatic portal vein tree: A Micro-CT Study. Ann Biomed Eng, 13, 2006) compared the radii and branching angles of the vessels to a theoretical model of dichotomous branching.
Software-based analysis and computation of the vector field of a vascular tree has traditionally been slow and cumbersome. Some methods begin with all voxels of a volumetric image and use a thinning technique to shrink down the object to a single line. Ideally, the topology of the object should be preserved as proposed by Lobregt et al. (Three-dimensional skeletonization: principle and algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2(1): 75-77, 1980), which is the basic technique used in commercial software systems, such as Analyze™ (AnalyzeDirect, Inc., Overland Park, Kans.). The disadvantage of this approach is that it tends to produce jagged lines which do not allow accurate measurements of branch angles. Luboz et al. (A segmentation and reconstruction technique for 3D vascular structures. MICCAI 2005, Lecture Notes in Computer Science 3749:43-50, 2005) used a thinning-based technique to determine vessel radii and lengths from a CTA scan. A smoothing filter was employed to eliminate the jaggedness of the thinning process and the results were validated using a silicon phantom. A standard deviation of 0.4 mm between the computed and the actual measurements was reported for a scan with similar resolution as that used in the embodiments of the disclosure of the present application.
The disadvantage of thinning algorithms is that they can only be applied to volumetric data sets. Since the approach presented herein is not based on voxels it can be applied to non-volumetric data; i.e., it is also applicable to geometric data sets, such as those obtained from laser scans. Furthermore, the location of the centerline is determined at a higher numerical precision since its defining points are not bound to a single voxel. This also helps avoid the jagged representation of the centerlines.
Other approaches use the distance transform or distance field in order to obtain a curve-skeleton. For each point inside the object, the smallest distance to the boundary surface is determined. For example, fast marching methods can be employed to compute the distance field. Voxels representing the centerlines of the object are identified by finding ridges in the distance field. The resulting candidates must then be pruned first. The resulting values are connected using a path connection or minimum span tree algorithm. The distance field can also be combined with a distance-from-source field to compute a skeleton. Similar to thinning approaches, these methods are voxel-based and tend to generate the same jagged centerlines. This implies that a centerline can deviate from its original location by up to half a voxel due to the numerical representation. The approach of the disclosure of the present application does not suffer from this problem as it uses a higher numerical precision for the determination of centerlines.
A more recent method by Cornea et al. (Computing hierarchical curve-skeletons of 3D objects. The Visual Computer, 21(11):945-955, 2005) computes the distance field based on a potential similar to an electrical charge and then uses a 3D topological analysis to determine the centerlines. This approach, however, suffers from a few disadvantages when applied to CT scanned volumetric images. For example, it is computationally intensive such that computing the distance field alone would take several months. Furthermore, due to the rare occurrence of 3D singularities used as starting point for topological analysis, additional criteria have to be imposed. The method of the disclosure of the present application avoids this by linearly interpolating the vector field within the vessels and by performing a two-dimensional (2D) topological analysis in cross sections of the vessels only. This results in a significantly shorter computational time for generation of data which is very important for large data sets.
In addition to the foregoing, techniques based on Voronoi diagrams define a medial axis using the Voronoi points. Since this approach usually does not result in a single line but rather a surface shaped object, the points need to be clustered and connected in order to obtain a curve-skeleton. Voronoi-based methods can be applied to volumetric images as well as point sets. Due to the fact that clustering of the resulting points is required, these approaches lack accuracy. In addition, they tend to create points outside the object itself if there is an open or missing area within the object's boundary. These methods usually tend to extract medial surfaces rather than single centerlines. Hence, clustering of the resulting points is required which in turn may introduce numerical errors.
For extracting centerlines from volumetric images, geometry-based approaches are preferable over voxel-based approaches. Due to the discrete nature of a voxel of the volumetric image, the location of the centerline can have an error of half a voxel. Geometry-based methods do not have this problem. Nordsletten et al. determined normal vectors based on an iso-surface computed using the volumetric image. These normal vectors are projected inward. The resulting point cloud is then collected and connected by a snake algorithm. Since this method estimates the normal vectors, the center of the vessel is not necessarily in the direction of the normal vector. Hence, the computed centerline may not be absolutely accurate. The disclosure of the present application utilizes a technique based upon a vector field analysis with vectors pointing toward the vessel center. This method disclosed herein is more lenient with regard to vector direction while still finding accurate center points. The technique of the disclosure of the present application compensates for this type of error automatically. It is therefore expected that a more precise computation of center points is possible. The approach based on a 3D vector field analysis proposed by Cornea et al. results in a very accurate computation of the centerlines. The only difficulty with this approach is that computing the centerlines for a CT scanned volumetric image of the size 512 by 512 by 200 would take several months, which renders it inapplicable.
What is needed is a technique for extracting vascular structures from volumetric images that does not suffer from some of the drawbacks of conventional methods, is efficient, easy to use, intuitive, and based on more physiological conditions than prior techniques.